Question

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?

Options

• `3/4` of original square.

• `1/2` of original square.

• `1/4` of original square.

• `2/3` of original square.

Answer 1

`bb(1/2 "of original square")`.

Explanation:

Let a be the side of a square sheet.

Then, area of bigger square sheet = a²  ...(i)

Now, we make the circle of maximum possible size from it.

Then, the radius of circle = `a/2`  ...(ii)

So, its diameter (d) = `2 * a/2 = a`

Now, any square in a circle of maximum size will have the length of diagonal equal to the diameter of circle.

i.e Diagonal of square made inside the circle = a

So, the side of this square = `a/sqrt(2)`   ...[∵ Diagonal = side `sqrt(2)`]

∴ Area of this square = `a^2/2`  ...(iii)

From equations (i) and (iii),

Area of final square is `1/2` of original square.